How to control object's path follow speed based on its position
One way to do it is to use a discretized implementation instead of a parameterized one. We store the parameter (location along spline) of the object in a custom property. At each execution, we increment that parameter by the velocity that we can compute from the relation you provided above.



The divide node is a unit conversion which you can replace with whatever you need. Note that Uniform has to be used when sampling the location for obvious reasons.

A useful addition is to add a condition where the parameter is set back to zero whenever the frame is equal to or less than one so that you can play the animation as much as you want.



A similar condition can be added to cube location.